This research analyzes the role of the University in incremental innovation in processes, products and radical innovation of the firm as part of the adoption of open innovation. Using a sample of 344 Spanish firms in the industrial and services sectors, it is observed that University support innovation services to improve innovative activity of firms that hire those services: whether specific services directly related (professional services, studies academic research, use of infrastructure and equipment) as well as the hiring of training activities (continuous training). However, the increased of professionals in the company or foster open innovation does not appear to influence, in general, a greater effect of these university services on incremental innovation. To the contrary, have a substitution effect on radical innovation when it comes to hiring the University of professional services.

Key words: incremental innovation, radical innovation, University-Firm.
JEL Classification: I2/L2/M1/M2/M5/O3.